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## Potential ApproximationThe simplest Taylor approximation of a function f which has multiple parameters is: (where H is the Hesse Matrix) In Electrodynamics, functions of the following form appear for the electrostatic potential: An example is: How do we calculate the value of this function? In order to find out, we develop the function into a Taylor Series with development point . We now actually plug the function in: So, what is ? Hence, Let . Then, So, what is ? Hence, After plugging this into the original integral: With: Monopole momentum
Dipole momentum
Quadrupole momentum
Author: Danny (remove the ".nospam" to send) Last modification on: Sat, 04 May 2024 . |